{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [625, 125, 25, 5, 1], [500, 75, 10, 1, 0], [16, 8, 4, 2, 1]]\n",
      "[3, 0, 9, 0, 1]\n",
      "[[-1.14222222e-01  1.04622222e+00 -2.13555556e+00  1.00256886e-15\n",
      "   3.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "a1 = []\n",
    "a1.append([0,0,0,0,1])\n",
    "a1.append([0,0,0,1,0]) \n",
    "a1.append([5**4,5**3,5**2,5,1])\n",
    "a1.append([4*(5**3),3*(5**2),2*5,1,0])\n",
    "a1.append([2**4,2**3,2**2,2,1])\n",
    "# a1.append([4*(2**3),3*(2**2),2*2,1,0])\n",
    "v_m = 0\n",
    "v_f = 0 \n",
    "print (a1)\n",
    "b1 = [3,0,9,v_f,1]\n",
    "print (b1)\n",
    "a1 = np.array(a1)\n",
    "b1 = np.array(b1)\n",
    "x = np.dot(np.linalg.pinv(a1),b1.T)\n",
    "x = np.array(x)\n",
    "x = np.expand_dims(x, axis=0)\n",
    "print (x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [625, 125, 25, 5, 1], [500, 75, 10, 1, 0], [16, 8, 4, 2, 1]]\n",
      "[[ 2.05555556e-02 -2.85555556e-01  1.11388889e+00  6.41560003e-16\n",
      "   6.15070027e-16]]\n"
     ]
    }
   ],
   "source": [
    "a2 = []\n",
    "a2.append([0,0,0,0,1])\n",
    "a2.append([0,0,0,1,0]) \n",
    "a2.append([5**4,5**3,5**2,5,1])\n",
    "a2.append([4*(5**3),3*(5**2),2*5,1,0])\n",
    "a2.append([2**4,2**3,2**2,2,1])\n",
    "# a2.append([4*(2**3),3*(2**2),2*2,1,0])\n",
    "print (a2)\n",
    "b2 = [0,0,5,0,2.5]\n",
    "a2 = np.array(a2)\n",
    "b2 = np.array(b2)\n",
    "y = np.dot(np.linalg.pinv(a2),b2.T)\n",
    "y = np.expand_dims(y, axis=0)\n",
    "print (y)\n",
    "points1 = [3,1,9]\n",
    "points2 = [0,2.5,5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50,)\n",
      "(5, 50)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 720x720 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure = plt.figure(figsize = (10,10))\n",
    "t = np.linspace(0,5,50)\n",
    "print (t.shape)\n",
    "tbig = np.vstack((t**4,t**3,t**2,t,np.ones(50)))\n",
    "xc = x @ tbig\n",
    "yc = y @ tbig\n",
    "print(tbig.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xc.T,yc.T)\n",
    "plt.title('Trajectory')\n",
    "plt.scatter(points1,points2,s=100)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50,)\n",
      "(5, 50)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0,5,50)\n",
    "print (t.shape)\n",
    "tbig_diff = np.vstack((4*(t**3),3*(t**2),2*t,np.ones(50),np.zeros(50)))\n",
    "print(tbig_diff.shape)\n",
    "xc_diff = x @ tbig_diff\n",
    "yc_diff = y @ tbig_diff\n",
    "plt.plot(yc_diff.T)\n",
    "plt.title('Velocity in y direction')\n",
    "\n",
    "plt.show()\n",
    "plt.plot(xc_diff.T)\n",
    "plt.title('Velocity in x direction')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50,)\n",
      "(5, 50)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0,5,50)\n",
    "print (t.shape)\n",
    "tbig_diff = np.vstack((12*(t**2),6*t,2*np.ones(50),np.zeros(50),np.zeros(50)))\n",
    "print(tbig_diff.shape)\n",
    "xc_diff = x @ tbig_diff\n",
    "yc_diff = y @ tbig_diff\n",
    "plt.plot(yc_diff.T)\n",
    "plt.title('Acceleration in y direction')\n",
    "\n",
    "plt.show()\n",
    "plt.plot(xc_diff.T)\n",
    "plt.title('Acceleration in x direction')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 0], [0.07775999999999998, 0.2592, 0.3456, 0.23040000000000005, 0.07680000000000002, 0.010240000000000003], [-0.1296, -0.21599999999999997, 0.0, 0.19200000000000003, 0.12800000000000003, 0.025600000000000005], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, -1, 1]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 720x720 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Bernstein polynomial\n",
    "import copy\n",
    "figure = plt.figure(figsize = (10,10))\n",
    "w = []\n",
    "\n",
    "tau = 0\n",
    "w.append([(1-tau)**5,5*tau*((1-tau)**4),10*((tau)**2)*(1-tau)**3,10*(tau)**3*(1-tau)**2,5*(tau)**4*(1-tau),tau**5])\n",
    "w.append([-1*(1-tau)**4,(1-tau)**3*(1-5*tau),2*tau*(1-tau)**2*(2-5*tau),2*tau**2*(1-tau)*(3-5*tau),(tau**3)*(4-5*tau),tau**4])\n",
    "\n",
    "tau = 2/5\n",
    "w.append([(1-tau)**5,5*tau*((1-tau)**4),10*((tau)**2)*(1-tau)**3,10*(tau)**3*(1-tau)**2,5*(tau)**4*(1-tau),tau**5])\n",
    "w.append([-1*(1-tau)**4,(1-tau)**3*(1-5*tau),2*tau*(1-tau)**2*(2-5*tau),2*tau**2*(1-tau)*(3-5*tau),(tau**3)*(4-5*tau),tau**4])\n",
    "\n",
    "v_m = 0\n",
    "v_f = 0\n",
    "\n",
    "tau = 1\n",
    "w.append([(1-tau)**5,5*tau*((1-tau)**4),10*((tau)**2)*(1-tau)**3,10*(tau)**3*(1-tau)**2,5*(tau)**4*(1-tau),tau**5])\n",
    "w.append([-1*(1-tau)**4,(1-tau)**3*(1-5*tau),2*tau*(1-tau)**2*(2-5*tau),2*tau**2*(1-tau)*(3-5*tau),(tau**3)*(4-5*tau),tau**4])\n",
    "b = [3,0,1,v_m,9,v_f]\n",
    "print(w)\n",
    "w = np.array(w)\n",
    "b1 = np.array(b)\n",
    "w2 = copy.deepcopy(w)\n",
    "b2 = [0,0,2.5,v_m,5,v_f]\n",
    "b2 = np.array(b2)\n",
    "\n",
    "y1 = np.dot(np.linalg.pinv(w),b1.T)\n",
    "y1 = np.expand_dims(y1, axis=0)\n",
    "y2 = np.dot(np.linalg.pinv(w2),b2.T)\n",
    "y2 = np.expand_dims(y2, axis=0)\n",
    "points1 = [3,1,9]\n",
    "points2 = [0,2.5,5]\n",
    "figure = plt.figure(figsize = (10,10))\n",
    "t = np.linspace(0,5,50)\n",
    "tbig = np.vstack(((1-(t/5))**5,t*(1-(t/5))**4,10*((t/5)**2)*(1-(t/5))**3,10*((t/5)**3)*(1-(t/5))**2,((t/5)**4)*(5-t),(t/5)**5))\n",
    "yc = y1 @ tbig\n",
    "yc1 = y2 @ tbig\n",
    "plt.plot(yc.T,yc1.T)\n",
    "plt.scatter(points1,points2,s=100)\n",
    "plt.grid()\n",
    "plt.title('Position for Bernstein Polynomial')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50,)\n",
      "(6, 50)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#for velocity\n",
    "t = np.linspace(0,5,50)\n",
    "print (t.shape)\n",
    "tbig_diff_2 = np.vstack((-1*(1-t/5)**4,(1-t/5)**3*(1-t),2*t/5*(1-t/5)**2*(2-t),2*(t/5)**2*(1-t/5)*(3-t),(t/5)**3*(4-t),(t/5)**4))\n",
    "print(tbig_diff_2.shape)\n",
    "xc_diff_2 = y1 @ tbig_diff_2\n",
    "yc_diff_2 = y2 @ tbig_diff_2\n",
    "plt.plot(yc_diff_2.T)\n",
    "plt.title('Velocity in y direction')\n",
    "\n",
    "plt.show()\n",
    "plt.plot(xc_diff_2.T)\n",
    "plt.title('Velocity in x direction')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50,)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#for acceleration\n",
    "t = np.linspace(0,5,50)\n",
    "print (t.shape)\n",
    "# tbig_diff_3 = np.vstack((4/5*(1-t/5)**3,-3/5*(1-(t/5)**2)*(1-t)-(1-t/5)**3,2/5*((1-t/5)**2*(2-2*t)-2*(2*t/5-5*(t/5)**2)*(1-t/5)),2/5*t/5*(20*(t/5)**2-24*(t/5)+6),12/5*(t/5)**2-4*(t/5)**3,4*(t/5)**3))\n",
    "tbig_diff_3 = np.vstack((4/5*(1-t/5)**3,-3/5*(1-(t/5)**2)*(1-t)-(1-t/5)**3,-2/5*((1-t/5)*(4*t/5-2*t**2/5)+(1-t/5)**2*(4/5-4*t/5)),-1/5*((6*t**2-2*t**2)/25)+(1-t/5)*(12*t/25-6*t/25),(12*t**2 - 4*t**3)/125,(4*(t)**3)/625))\n",
    "\n",
    "# print(tbig_diff_2.shape)\n",
    "xc_diff_3 = y1 @ tbig_diff_3\n",
    "yc_diff_3 = y2 @ tbig_diff_3\n",
    "plt.plot(yc_diff_3.T)\n",
    "plt.title('Acceleration in y direction')\n",
    "\n",
    "plt.show()\n",
    "plt.plot(xc_diff_3.T)\n",
    "plt.title('Acceleration in x direction')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [625, 125, 25, 5, 1], [500, 75, 10, 1, 0], [16, 8, 4, 2, 1], [0, 0, 2, 0, 0]]\n",
      "[3, 0, 9, 0, 1, 1.7777777777777777]\n",
      "[[-0.0337822   0.18167175  0.49102305 -1.43231701  2.09286589]]\n"
     ]
    }
   ],
   "source": [
    "#Bonus\n",
    "#done using quartic polynomial, adding more constraints\n",
    "a1 = []\n",
    "a1.append([0,0,0,0,1])\n",
    "a1.append([0,0,0,1,0]) \n",
    "a1.append([5**4,5**3,5**2,5,1])\n",
    "a1.append([4*(5**3),3*(5**2),2*5,1,0])\n",
    "a1.append([2**4,2**3,2**2,2,1])\n",
    "# t = 2.5\n",
    "# a1.append([t**4,t**3,t**2,t,1])\n",
    "# t = 3\n",
    "# a1.append([t**4,t**3,t**2,t,1])\n",
    "# t = 4.5\n",
    "# a1.append([t**4,t**3,t**2,t,1])\n",
    "# t = 2.5\n",
    "# a1.append([4*t**3,3*t**2,2*t,1,0])\n",
    "# t = 3\n",
    "# a1.append([4*t**3,3*t**2,2*t,1,0])\n",
    "# t = 4.5\n",
    "# a1.append([4*t**3,3*t**2,2*t,1,0])\n",
    "t = 0\n",
    "a1.append([12*t**2,6*t,2,0,0])\n",
    "v_m = 0\n",
    "v_f = 0 \n",
    "print (a1)\n",
    "# b1 = [3,0,9,v_f,1,2.2,2.5,7,0,0,0,16/9]\n",
    "b1 = [3,0,9,v_f,1,16/9]\n",
    "print (b1)\n",
    "a1 = np.array(a1)\n",
    "b1 = np.array(b1)\n",
    "x = np.dot(np.linalg.pinv(a1),b1.T)\n",
    "x = np.array(x)\n",
    "x = np.expand_dims(x, axis=0)\n",
    "print (x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [625, 125, 25, 5, 1], [500, 75, 10, 1, 0], [16, 8, 4, 2, 1], [0, 0, 2, 0, 0]]\n",
      "[[ 0.00570577 -0.12595357  0.62900434  0.26441561  0.16746322]]\n"
     ]
    }
   ],
   "source": [
    "a2 = []\n",
    "a2.append([0,0,0,0,1])\n",
    "a2.append([0,0,0,1,0]) \n",
    "a2.append([5**4,5**3,5**2,5,1])\n",
    "a2.append([4*(5**3),3*(5**2),2*5,1,0])\n",
    "a2.append([2**4,2**3,2**2,2,1])\n",
    "\n",
    "# t = 2.5\n",
    "# a2.append([t**4,t**3,t**2,t,1])\n",
    "# t = 3\n",
    "# a2.append([t**4,t**3,t**2,t,1])\n",
    "# t = 4.5\n",
    "# a2.append([t**4,t**3,t**2,t,1])\n",
    "# t = 2.5\n",
    "# a2.append([4*t**3,3*t**2,2*t,1,0])\n",
    "# t = 3\n",
    "# a2.append([4*t**3,3*t**2,2*t,1,0])\n",
    "# t = 4.5\n",
    "# a2.append([4*t**3,3*t**2,2*t,1,0])\n",
    "t = 0\n",
    "a2.append([12*t**2,6*t,2,0,0])\n",
    "print (a2)\n",
    "\n",
    "# b2 = [0,0,5,0,2.5,2.7,3.7,4,0,4,6,10/9]\n",
    "b2 = [0,0,5,0,2.5,10/9]\n",
    "a2 = np.array(a2)\n",
    "b2 = np.array(b2)\n",
    "y = np.dot(np.linalg.pinv(a2),b2.T)\n",
    "y = np.expand_dims(y, axis=0)\n",
    "print (y)\n",
    "points1 = [3,1,9,5]\n",
    "points2 = [0,2.5,5,4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50,)\n",
      "(5, 50)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 720x720 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure = plt.figure(figsize = (10,10))\n",
    "t = np.linspace(0,5,50)\n",
    "print (t.shape)\n",
    "tbig = np.vstack((t**4,t**3,t**2,t,np.ones(50)))\n",
    "xc = x @ tbig\n",
    "yc = y @ tbig\n",
    "print(tbig.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xc.T,yc.T)\n",
    "plt.scatter(points1,points2,s=100)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
